Temperature effects on the growth of the Co adsorbates on Pt vicinal surface

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Physics Procedia 00 (2008) 000–000 Physics Procedia 2 (2009) 865–872 www.elsevier.com/locate/XXX www.elsevier.com/locate/procedia

Proceedings of the JMSM 2008 Conference

Temperature effects on the growth of the Co adsorbates on Pt vicinal surface H. Garbouja*, M. Saida, F. Picaud b, Ch. Ramseyerb a

Département de Physique, Université de Monastir, Faculté des Sciences de Monastir, UR1319, 5019 Monastir, Tunisie b UTINAM-B, UMR 6213, UFR-ST, Université de Franche-Comté, 25030 Besançon, France

Elsevier2009; use only: Received date here;form revised accepted date 31 hereAugust 2009 Received 1 January received in revised 31 date Julyhere; 2009; accepted

Abstract Kinetic Monte Carlo simulations based on semi empirical description of Co-Pt interactions are developed to describe all the kinetic processes appearing on the Pt (997) vicinal surface and to highlight the temperature effect on the growth of the Co adsorbates. Depending on temperatures, three regimes are found. For law temperature, T” 50 K, the nucleation regime is dominant, small islands are randomly dispersed on the Pt vicinal surface and the number of islands increases regularly. For the narrow temperature range [100, 150] K, the growth regime takes place, where the islands number stabilizes and the islands sizes increases. For high temperature, T• 200 K, the coalescence regime is dominant. The number of islands decreases and the size of islands increases. We have also studied the site occupation at the step edge compared to the surface occupation as a function of the deposited adatoms in order to emphasize the step influence on the growth of Co on Pt (997) for different temperatures. © 2009 Elsevier B.V. All rights reserved PACS:71.20.Be/71.15.Pd/74.78.-w/78.67.Bf. Keywords: vicinal surface/nucleation/growth/islands/coalescence/Diffusion/KMC simulation

1. Introduction Nucleation and growth of mono-disperse nanostructures is a challenging field both for theoretical modeling [1-6] and practical applications due to their new magnetic [7], electric [8] and catalytic [9] properties [10]. The use of spontaneously nanostructured substrates as templates for organized growth is a promising way [11] since it allows growing not only regular nanostructures but also high density nanostructures. This opens up new studies of both individual and collective physical properties by means of standard averaging techniques. Metal on metal growth provides model systems for ordered growth on well-defined nano-patterned substrates [12-14]. Experimentally, this phenomenon has been successfully applied to the formation of nanostructures [15-18]. The precise determination of the atomistic mechanisms for a given substrate should allow to make prediction in

* Corresponding author. Tel.: +216-97 221 146 E-mail address: [email protected]

doi:10.1016/j.phpro.2009.11.037

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order to get an ordered growth with various deposited materials and to find out the conditions (flux, temperature) [19] for achieving the narrowest size distribution. When a metal on metal epitaxial film is grown, atoms arrive at the substrate surface individually and move around on it randomly. Initially the concentration of lone atoms rises. The free energy of this sea of adatoms is reduced by the aggregation of monomers to form islands [20]. Once these islands have been nucleated, additional atoms arriving at the surface are more likely to encounter an island than another diffusing monomer. Thus, existing islands grow with little further nucleation of new islands [21]. Eventually these islands coalesce and a contiguous film is formed [20]. The kinetic of this process is limited by the time taken for diffusing monomers to collide with other monomers or relatively immobile islands. Here we propose to study the kinetic of Co adsorbed on stepped Pt (997) in order to explain the role of the defects in the growth regimes. In part II we describe the theoretical model used in this study while part III is focused on the KMC results. 2. Structural and interaction model Pt (997) is a stepped surface with a remarkable uniformity. This surface is constituted by monatomic steps (often quoted as B steps in the literature) that separate terraces of (111) orientation with a 20.1 Å average width (8 atomic rows) and (111) ledges as shown in Figure 1 [22]. (111) (111) 20.1 Å

Fig.1: Pt (997) vicinal surface representation [22].

The interactions between the adsorbate (Co) and substrate (Pt) system have been modeled with a modified version [23] of the semi-empirical potential proposed by Rosato et al. [24]. The latter potential is based on a manybody description of the interactions and has proved successfully to interpret the properties of metals depending on the effective width of the electronic density of states. It has been derived from the tight-binding theory in the second moment approximation [25] and is therefore well-suited for transition metals exhibiting a narrow d band and to a less extent to noble species [26, 27]. It is expressed as a sum of exponential terms describing the repulsive contribution assumed to be pair wise and the non-additive attractive interactions. The total potential energy between atoms is written as: V=

ª § rij ·º A IJ exp « − p IJ ¨¨ IJ − 1¸¸ » × f cIJ (rij ) − © r0 ¹ »¼ ¬« j , rij ¢ rcIJ

¦¦ i

­° ½ ª º r (ξ IJ )1α exp «− 2q IJ §¨¨ ijIJ − 1·¸¸» × f cIJ (rij )°¾ ® © r0 ¹»¼ °¯ j,rij ¢ rcIJ °¿ ¬«

α

¦ ¦ i

(1)

where rij is the distance between two atoms at sites i and j. I and J indicate the chemical species: I, J =Co or Pt, r0II IJ II JJ is the first nearest neighbor distance in the metal I and r0 = (r0 + r0 ) / 2 . The term qIJ characterizes the distance ξ IJ is an effective hopping dependence of the hopping integrals between atoms I and J at sites i and j, respectively. integral. The parameters AIJ and pIJ determine the repulsive part of the interaction and fcIJ (rij) is a cut-off

function. In the bulk metals, the interactions are limited to first (r0II) and second (

2 r0II

) nearest neighbors, i.e.

2 r0II

r² = =1 =0 and when . However, in the present study, some interatomic distances are allowed to vary continuously. Therefore we must define a cut-off function which takes the above values in the f cII (r0II )

f cII (

2 r0II )

f cII (r )

bulk metals and are continuous as well as their first two derivatives for any rij. This ensures a smooth variation of the total energy and of the forces which is here absolutely needed since dramatic effects may occur if an abrupt cutoff is used when an interatomic distance crosses the cut-off distance. We have chosen the function:

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H. Garbouj et al. / Physics Procedia002(2009) (2009)000–000 865–872 Hedi Garbouj/ Physics Procedia IJ f cIJ ( rij ) = 1 when rij ¢ rmin

(2)

1 1 IJ IJ f cIJ ( rij ) = − sin (π .x ) when rmin ¢ rij ¢ rmax 2 2

(3)

IJ f cIJ ( rij ) = 0 when rij ² rmax

rij − ¢ r

x =

Δ r

IJ

IJ

²

(4)

, r mI Ji n =

2 r 0I J + 0 . 1 Å , r mI Ja x =

3 r 0I J − 0 . 1 Å

¢ r ² represents the point located at the average position of r IJ and r IJ ( r IJ = rmin + rmax ). ǻrIJ is the mean min max 2 IJ IJ distance between this average and rmin (or rmax ). These two values allow us to change r ji as a centered-reduced variable x. Finally the value of Į derived from the tight-binding theory in the second moment approximation is Į=1/2. Note that a value Į=2/3 is sometimes used since it has been shown that this value simulates satisfactorily the influence of higher order moments and yields better surface energies [28].In our case, we have performed calculations using the two values of Į. However, Į = 2/3 was found to give overestimated dissociation barrier for the dimer [27] and thus non comparable values with growth experiments, especially for Co specie. For each pure metal species (Co and Pt), the parameters (A, p, q, ȟ) were determined by fitting the potential to the universal equation of state driving the variation of the potential with distance in the bulk, namely the equilibrium distances, the cohesive energies, the bulk moduli and elastic constants [26].We have also tried to reproduce the associated surface energies of each species. The fits have also been carried out by varying the weight given to surface energies. In addition, one can limit the calculation to an additional physical condition on the ratio p/q, namely, p/2Įq ” 5 [29]. Table 1 shows the potential parameters for the two metals with the corresponding fitted properties. The differences between calculated and experimental values are reasonable. Finally the parameters referring to heteroatomic bonds are taken as arithmetical and geometrical averages for (p, q) and (A, ȟ), respectively. This set of parameters will be used in the following to calculate the relevant energy barriers implemented in the KMC code. IJ

IJ

IJ

Table1: Parameters [A (eV), p, q, ȟ (eV)] of the potential (see Eq.1) for the pure Co or Pt metals and for the heteroatomic Co-Pt bonds. The fitted and experimental values (in eV/atom) of the cohesive energies Ecoh, bulk modulus B and surface energies Ȗ111, Ȗ110 and Ȗ100 for the low index surfaces are also given.

A

p

q

ȟ

p/2 Į q

Ecoh

B

Pt/Pt 0.204 Data from literature [24]

11.854 2.371

3.473

3.41

-5.86 27.09 -5.86 27.00

Co/Co 0.103 Data from literature [24]

11.083 1.577

2.386

4.64

-4.40 13.25 -4.39 13.25

Co/Pt

11.468 1.933

2.929

0.145

Ȗ111

Ȗ110

Ȗ100

0.53 1.03

1.10 1.69

0.70 1.19

0.50 0.96

0.98 2.46

0.61 1.98

-

As a first check of these parameters, we have also calculated the diffusion barriers for atoms moving on the Pt (997) surface. Indeed, it is well-known that single atom diffusion is the main process that guides the growth of islands on surfaces. An error in these barriers may drastically change the number, density and shape of the islands formed on the surface. Moreover, these values can be compared to experiments in some cases. Figure 2 represents the single atom diffusion by a hopping process between hcp and fcc sites. We have determined each point of this path by optimizing, with the conjugate gradient method, the total potential energy with respect to the degrees of freedom of the adsorbate.

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-3.25

-3.30 ED=0.223eV

Energy (eV)

-3.35

ED=0.230eV

-3.40

-3.45

-3.50

fcc

-3.55

hcp

-3.60 4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

X ( Å)

Fig.2: The single atom diffusion by a hopping process between hcp and fcc site. The diffusion barrier ED is equal to 0.230 eV (from hcp to fcc) and 0.223 eV (from fcc to hcp).

The substrate was assumed to be rigid even though we have found recently by density functional theory (DFT) that a small inward relaxation occurs for Pt atoms located near step edges [30]. Far from the step, on the terrace sites, we found that at hcp and fcc sites the adatom has nearly the same adsorption energy (fcc:-3.534 eV and hcp:3.541 eV for Co), the difference in energy ǻ hcp/fcc between hcp and fcc sites is very weak (7meV), the hcp site being more stable. Far from the step the diffusion barriers ED for Co adatom are equal to 0.230 eV (from hcp to fcc) and 0.223 eV (from fcc to hcp) and compare well with molecular dynamics calculations (with substrate relaxation) performed by Goyhenex [27] who finds ED = 0.210 eV, with no significant differentiation between hcp and fcc sites. Experimentally, a value of 0.21 eV for Co adatom diffusion on Pt is usually inferred from STM as well as field ion microscopy [27, 31] for Co atoms diffusing on Pt (111) terraces. The step influences the corrugation of the adsorption energy of the adatom over a rather short distance (2 or 3 rows are energetically perturbed by the step). At this stage, only monomer diffusion has been discussed. We have thus considered the attachment/detachment of atoms from islands. Figure 3 represents the diffusion barrier necessary for one Co atom to aggregate or dissociate from a given island (constituted from 4 atoms).This diffusion barrier changes drastically with the number of neighbors close to the diffusing atom. Indeed, when one Co atom diffuses from fcc site with 0 to 4 neighbors to an isolated hcp site, the barrier changes from 0.230 eV to 0.863 eV. This is easily understood since the presence of neighboring atoms at the initial site lowers both the energy of this site and, due to the range of potential which extends up to the third nearest neighbors, of the saddle point [32]. Obviously this lowering is more pronounced at the initial site so that the barrier height increases the more as the coordination number at the initial site is large. On the opposite, the barriers of attachment to a pre-existing island decrease and even vanish depending on the number of neighbors in the arrival site. We obtain for example no barrier for attachment of Co atom to an island edge with 4 atoms compared to 0.230 eV for the single diffusion barrier due to the range of the potential which reduces the adatom energy at the saddle point by the influence of the atoms with which it will be bound in the final state. Thus the higher the coordination of the final state, the lower the barrier. This means that during the growth, the capture of adatoms will be easier as soon as islands will be formed (islands look as traps for Co adatoms).

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-18.6

aggregation

-18.8

hcp

Energy (eV)

-19.0

-19.2

-19.4

-19.6 dissociation -19.8

fcc

-20.0 3.5

4.0

4.5

5.0

5.5

6.0

X (Å)

Fig.3: The diffusion barrier necessary for one Co atom to aggregate or dissociate from an island (constituted from 4 atoms). The barrier is equal to 0.863 eV (to dissociate) and 0 eV (to aggregate).

3. KMC simulations: role of the kinetic in the Co island formation KMC simulations play an increasing role in our understanding of atomistic details of epitaxial growth [33]. Very simple models are often employed to study qualitatively a particular physical problem for which only limited information (experimental or reliable microscopic calculations) is available. In the standard picture, atoms are deposited on a substrate with a flux F and diffuse onto the substrate with a temperature dependent diffusion coefficient D. No desorption is allowed. When two atoms or more meet irreversibly a 2D one monolayer island nucleates and grows further by the diffusion limited capture of adatoms. In our case, such a simple model cannot be used and a realistic picture of Co/Pt systems has to be drawn. We have thus used a sophisticated version of KMC to be as close as possible to reality and considered deposition, diffusion and complete reversible aggregation [33]. We have considered a deposition flux of 10-3 MLs-1, Co coverage ș= 0.6 ML and a set of temperatures sufficient to study their role on the islands formation. The geometry of the system has been introduced through the activation barriers discussed above. These latter barriers were introduced in the KMC with a probability following a simple Arrhenius law. There are thus as many processes as potential barriers in the simulation. Due to the negligible energy differences observed on the terraces, hcp and fcc sites are considered as equivalent in the growth simulations. It should be noted that desorption, diffusion of dimers and deposition onto preexisting islands were not considered here since they should not affect the growth significantly. However, we are aware that dimer diffusion can also occur in the light of the recent results reported by Goyhenex [27]. Indeed, this author shows that the diffusion of the Co dimer is enhanced on the Pt surface with respect to homoepitaxy (Pt dimers on Pt (111)). This is mainly due to the large lattice mismatch between Co and Pt. For further details on the KMC code, we refer the reader to ref. [23]. Depending on temperatures, three regimes are found for the growth of Co adatoms on the Pt vicinal surface. For low temperature, below 50 K, the nucleation regime starts for which no order is found as can be seen in figures 4 and 6 (snapshot (a)). Small islands are randomly dispersed on the surface and the monomer islands number is very high. We can notice that the positions of these adatoms seem not to be influenced by the particular surface structure (steps). The size of islands is remaining low and the smallest islands are most often found as it can be viewed on the size distributions plots for different substrate temperatures presented in figure 5. Between 100K and 150 K, an organization of the islands begins to appear (see snapshot Fig. 6(b)). However, as can be seen in figures 4 and 5, many islands are still randomly located on the surface but their number is stabilized and their size increases. For T• 200 K, the coalescence regime is dominant. Indeed, an organization clearly appears on the surface. The number of islands tends to decrease while their size increases a lot due to the capture of the smaller islands by the bigger one. The snapshots shown on Fig. 6 for ș = 0.6 ML summarize this discussion and give a very good idea about the

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morphology of the surface for different temperatures. At low temperature, the adatoms occupation is clearly random, the creation of new nucleation centers is favored, while at higher temperatures, and thanks to the easiest diffusion of monomers on the terraces, they reorganize themselves to form larger islands attached to the step.

1400

120 T=50 K T=100 K T=150 K T=200 K T=250 K T=300 K T=350 K

1000

T=50 K T=100 K T=150 K T=200 K T=250 K T=300 K T=350 K

100

80

Islands size

Islands number : N

1200

800

600

60

400

40

200

20

0 0

20

40

60

t(s)

Fig.4: The islands number of Co adatoms as a function of deposition time on the Pt vicinal surface for different temperatures.

80

0 0

20

40

60

80

t(s)

Fig.5: The average size of the islands of Co adatoms as a function of deposition time on the Pt vicinal surface for different temperatures.

Fig.6: Snapshots of 0.6 ML Co adatoms deposited on a (80ë80) Pt terrace at different temperatures with a deposition flux F=10-3 MLs-1.

Furthermore, to emphasize the influence of the coverage ș of Co adatoms sticking the surface and defined by the ratio between the deposited number ND of Co atoms and the number of available sites NTOT on the Pt (997) (ș = ND/NTOT), we calculated the site occupation NS at the step edge as a function of ND. Figure 7 (respectively Figure 8) represents NS (respectively the density D=NS/ND) as a function of ND (respectively ș). At low temperature and coverage, less than half of deposited adatoms are attached to the step NS§ND/2. When ș reaches a large value, NS tends to ND due to coalescence between small islands on terraces. However, for temperature higher than 150 K, the density D of adatoms tends towards saturation whatever the values of ș (NS§ND). Indeed, the Co adatoms have a kinetic energy sufficiently high to diffuse easily on the terraces and reach the more attractive well represented by the step edge (or the islands already coated to it). A thermodynamic equilibrium is obtained for these conditions. As a consequence, we demonstrate here that confinement can induce perfect step decoration only if kinetic effects are taken into account favorably.

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1.2

6000 T=100 K T= 150 K T=200 K T=300 K

5000

1.0

0.8

D

NS

4000

3000

0.6

2000

0.4

1000

0.2

T=100 K T=150 K T=200 K T=300 K

0.0

0 0

1000

2000

3000

N

4000

5000

6000

D

Fig.7: The number of Co adatoms ‘NS’ attached as single or aggregate adatoms to the step as a function of number of adatoms ‘ND’ deposed on the Pt vicinal surface

0.0

0.2

0.4

0.6

0.8

1.0

ș Fig.8: The density ‘D’of Co adatoms attached as single or aggregate adatoms to the step as a function of the coverage ‘ș’.

4. Conclusion We have developed both energy barrier calculations and KMC simulations to understand the influence of atom confinement on the growth process of Co atoms on the vicinal Pt (997) surface. The energy barriers are obtained from a semi-empirical model and reproduce quite well the previous experimental and theoretical data in the literature. These barriers are introduced in the KMC simulations to describe all the kinetic processes appearing on the surface. As a function of temperature, different regimes are found, the nucleation characterized by a high number of small islands dispersed on the Pt surface, the growth regime for which the islands number stabilizes and the islands sizes increases and the coalescence regime where the number of islands decreases and the size of islands increases. We have also studied the influence of the temperature and coverage effects on the growth of the adsorbed atoms, as a result, except for law temperature and coverage, the density D is practically independent of these parameters. References [1] J. A. Venables, Phys. Rev. B36 (1987) 4153. [2] G. S. Bales and A. Zangwill, Phys. Rev. B41 (1990) 5500. [3] J. G. Amar, F. Family, and P. M. Lam, Phys. Rev. B50 (1994) 8781. [4] M. C. Bartelt and J. W. Evans, Phys. Rev. B54 (1996) R17 359. [5] P. Jensen, H. Larralde, and A. Pimpinelli, Phys. Rev. B55 (1997) 2556. [6] J. W. Evans and M. C. Bartelt, Phys. Rev. B 66 (2002) 235410. [7] T.-Y. Lee, S. Sarbach, K. Kuhnke, and K. Kern, Surf. Sci. 600 (2006) 3266. [8] T. Ono and K. Hirose, Phys. Rev. Lett. 98 (2007) 026804. [9] N. Khan, H. Whu and J. Chen, J. Catalys. 205 (2002) 259. [10] J.G. Chen and C.A. Menning and M.B. Zellner, Surf. Sci. Rep. 63 (2008) 201. [11]. P. Gambardella and K. Kern, Surf. Sci. Lett. 475 (2001) L229. [12] D. Chambliss, R. Wilson, S. Chiang, Phys. Rev. Lett. 66 (1991) 1721. [13] H. Brune, M. Giovannini, K. Bromann and K. Kern, Nature 394 (1998) 451. [14] H. Ellmer, V. Repain, M. Sotto and S. Rousset, Surf. Sci. 511 (2002) 183. [15] P. Gambardella, M. Blanc, H. Brune, K. Kuhnke and K. Kern, Phys. Rev. B61 (2000) 2254. [16] P. Gambardella, A. Dallmeyer, K. Maiti, M.C. Malagoli, W. Eberhardt, K. Kern and C. Carbone, Nature 416 (2002) 301. [17] P. Gambardella, A. Dallmayer, K. Maiti, M.C. Malagoli, S. Rusponi, P. Ohresser, W. Eberhardt, C. Carbone andK. Kern, Phys. Rev. Lett. 93 (2004) 077203. [18] P. Gambardella, M. Blanc, L. Burgi, K. Kuhnke and K. Kern, Surf. Sci. 449 (2000) 93. [19] F. Picaud, C. Ramseyer, C. Girardet, H. Brune and K. Kern, Surf. Sci. 553 (2004) L68. [20] H. Röder, E. Hahn, H. Brune, J.P. Bucher and K. Kern, Nature 366 (1993) 141. [21] P. Jensen, Rev. Mod. Phys. 71 (1999) 1695. [22] K. Kuhnke and K Kern J. Phys.: Condens. Matter 15 (2003) S3311–S3335.

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